I am a bit confused with the Fourier series. The first step should be to determine if my function is odd or even, then find the coefficients (with eventually the shortcut for odd or even function) and finally I can compute the series.
My confusion comes from this exercise, where the function f with periodicity 2$\pi$ is given in the interval $0\le x\le2\pi $ as:
$f(x)= \left\{ \begin{array}{ll} x\ \text{for} \ 0\le x\le\pi\\ 0 \ \text{for}\ \pi\le x < 2\pi \end{array} \right.$
I thought that the function was odd, at least for the first interval, so I computed the Fourier series only by looking at the coefficient $b_n$ (I assumed that $a_n$ was 0).
I got the answer back from the TA saying that it's wrong, because $f(x)$ is neither odd nor even and therefore, the Fourier series should be computed with no shortcuts.
So my questions are:
1) Is possible for a function to be neither odd nor even?
2) Has this something to do with the discontinuity? How do you evaluate if a function is odd or even if the function is piecewise?
I feel like I must have missed some important concept about that.